In a saucepan, mix the mushroom and vegetable broths and bring to a simmer; keep warm.

In a large enameled cast-iron casserole, heat 1 tablespoon of the olive oil. Add the mushrooms, season with salt and pepper and cook over moderately high heat, stirring occasionally, until golden, about 5 minutes. Transfer to a bowl.

Add 1 tablespoon of the olive oil to the casserole. Add the kale and cook over moderate heat until wilted, 3 minutes. Add the kale to the mushrooms.

In the casserole, melt 1 tablespoon of the butter in the remaining 2 tablespoons of olive oil. Add the onion, season with salt and pepper and cook over moderate heat until softened, about 5 minutes. Add the rice and stir until coated with oil and lightly toasted, 2 minutes. Add the wine and cook, stirring, until evaporated. Add 2 cups of the hot broth, cover partially and cook, stirring occasionally, until most of the broth has been absorbed, 10 minutes. Repeat with another 2 cups of broth.

Add 3 cups of the broth, 1 cup at a time, and cook, stirring often, until it is mostly absorbed between additions, about 15 minutes total. Add the last cup of broth, the mushrooms, kale, thyme, 1/3 cup of cheese and the remaining 1 tablespoon of butter. Cook, stirring, until the risotto is creamy. Season with salt and pepper. Drizzle with oil and serve with cheese.